These five clowns work in pairs. What is the same and what is different about each pair's faces?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

A jigsaw where pieces only go together if the fractions are equivalent.

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

If a sum invested gains 10% each year how long before it has doubled its value?

Compares the size of functions f(n) for large values of n.

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Build up the concept of the Taylor series

Pupils at St Mary's in Tetbury approached the second part of this problem in a very logical (or systematic) way.

Nicole from Eastwood Primary describes a very sensible way of tackling this jigsaw.

Aleksander from Poland has just solved this Tough Nut. He had to simplify an algebraic expression, differentiate to find stationary points and solve a quadratic equation. Well done!

Three photographs each showing some measuring equipment. Can you work out what they are for?

A game in which players take it in turns to choose a number. Can you block your opponent?

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.